Quantum magnetism and quantum phase transitions

Abstract:

We report inelastic neutron scattering measurements of the spin dynamics in the layered hexagonal magnet 2H-AgNiO2 which has stacked triangular layers of antiferromagnetically-coupled Ni2+ spins (S=1) ordered in a collinear alternating stripe pattern. We observe a broad band of magnetic excitations above a small gap of 1.8 meV and extending up to 7.5 meV, indicating strongly dispersive excitations. The measured dispersions of the boundaries of the powder-averaged spectrum can be quantitatively explained by a linear spin-wave dispersion for triangular layers with antiferromagnetic nearest- and weak next-nearest neighbor couplings, a strong easy-axis anisotropy and additional weak inter-layer couplings. The resulting dispersion relation has global minima not at magnetic Bragg wavevectors but at symmetry-related soft points and we attribute this anomalous feature to the strong competition between the easy-axis anisotropy and the frustrated antiferromagnetic couplings. We have also calculated the quantum corrections to the dispersion relation to order 1/S in spin-wave theory by extending the work of Chubukov and Jolicoeur [Phys. Rev. B v46, 11137 (1992)] and find that the presence of easy-axis anisotropy significantly reduces the quantum renormalizations predicted for the isotropic model.

Abstract:

The excitations of the 2D Heisenberg antiferromagnet, Rb 2MnF4, were studied using neutron scattering techniques with the MAPS spectrometer at the ISIS facility of Rutherford Appleton Laboratory. Measurements were made of the magnetic excitations over the whole 2D Brillouin zone at 6 temperatures below the ordering temperature of 38 K and 6 temperatures above. It was found that the excitations were well defined if their wave vectors were larger than the inverse correlation length and were overdamped if the wave vectors of the excitations were smaller than the inverse correlation length. In more detail we have compared our experimental results with the results of classical simulations and the results gave a very adequate description of the experimental results except at the lowest temperature where the form of the dispersion relation was correct but the energies of the excitations were in error. Nevertheless, classical simulations do provide an effcient and easily implemented methodology for modelling the excitations in the Heisenberg magnets. The damping of the excitations was experimentally found to follow a T² behaviour over all wave vector and energy scales. This is in agreement with the classical simulations but inconsistent with analytic theories of the damping for the 2D Heisenberg model and in particular does not agree with hydrodynamic behaviour or dynamic scaling. The result is similar to that found in 3D Heisenberg systems and suggests that more analytic theory is needed to explain the experimental results for both 2D and 3D Heisenberg magnets.

Abstract:

We report 133Cs nuclear magnetic resonance (NMR) measurements of magnetic insulator Cs2CuCl4 in the paramagnetic phase (T≥4.2 K) as a function of the orientation of an applied magnetic field with respect to the principal crystalline axes. The magnetic shift tensor is determined. It is found that its principal axes do not coincide with the principal axes of the crystal. The Cu-Cs dipolar interaction tensor is calculated as well. From these, we deduce the full transferred hyperfine tensor for the two inequivalent Cs sites of the unit cell. We find that the tensors are anisotropic, containing non-zero off-diagonal terms, and that the transferred hyperfine coupling between Cu electronic spins and Cs nuclei dominates the NMR shift on both Cs sites. © 2008 IOP Publishing Ltd.

Abstract:

We report comprehensive inelastic neutron scattering measurements of the magnetic excitations in the 2D spin-5/2 Heisenberg antiferromagnet Rb2MnF4 as a function of temperature from deep in the Neel ordered phase up to paramagnetic, 0.13 < kBT/4JS < 1.4. Well defined spin-waves are found for wave-vectors larger than the inverse correlation length $\eta^{-1}$ for temperatures up to near the Curie-Weiss temperature, $\Theta_{CW}$. For wave-vectors smaller than $\eta^{-1}$, relaxational dynamics occurs. The observed renormalization of spin-wave energies, and evolution of excitation line-shapes, with increasing temperature are quantitatively compared with finite-temperature spin-wave theory, and computer simulations for classical spins. Random phase approximation calculations provide a good description of the low-temperature renormalisation of spin-waves. In contrast, lifetime broadening calculated using the first Born approximation shows, at best, modest agreement around the zone boundary at low temperatures. Classical dynamics simulations using an appropriate quantum-classical correspondence were found to provide a good description of the intermediate- and high-temperature regimes over all wave-vector and energy scales, and the crossover from quantum to classical dynamics observed around $\Theta_{CW}/S$, where the spin S=5/2. A characterisation of the data over the whole wave-vector/energy/temperature parameter space is given. In this, $T^2$ behaviour is found to dominate the wave-vector and temperature dependence of the line widths over a large parameter range, and no evidence of hydrodynamic behaviour or dynamical scaling behaviour found within the accuracy of the data sets.